TY - JOUR
ID - 4263
TI - Concerning the frame of minimal prime ideals of pointfree function rings
JO - Categories and General Algebraic Structures with Applications
JA - CGASA
LA - en
SN - 2345-5853
AU - Dube, Themba
AD - Department of Mathematical Sciences, University of South Africa, P.O.
Box 392, 0003 Unisa, South Africa.
Y1 - 2013
PY - 2013
VL - 1
IS - 1
SP - 11
EP - 26
KW - frame
KW - ring of real-valued continuous functions on a
frame
KW - minimal prime ideal
KW - basically disconnected
DO -
N2 - Let $L$ be a completely regular frame and $mathcal{R}L$ be the ring of continuous real-valued functions on $L$. We study the frame $mathfrak{O}(Min(mathcal{R}L))$ of minimal prime ideals of $mathcal{R}L$ in relation to $beta L$. For $Iinbeta L$, denote by $textit{textbf{O}}^I$ the ideal ${alphainmathcal{R}Lmidcozalphain I}$ of $mathcal{R}L$. We show that sending $I$ to the set of minimal prime ideals not containing $textit{textbf{O}}^I$ produces a $*$-dense one-one frame homomorphism $beta Ltomathfrak{O}(Min(mathcal{R}L))$ which is an isomorphism if and only if $L$ is basically disconnected.
UR - https://cgasa.sbu.ac.ir/article_4263.html
L1 - https://cgasa.sbu.ac.ir/article_4263_6f79ee547811c22128d166583042a1da.pdf
ER -